$(30\%)$

$(3)$ Two shafts mesh through their respective gears as illustrated in the figure. Calculate the total

mass moment of inertia of the system transferred to the top shaft as shown at ${}_1.($Bearings

are stationary; their masses will not contribute to the mass moment of inertia of the dynamic

system.$)$

Assume Shaft $1$ and Shaft $2$ have the same mass density $=100000\frac{kg}{m^3},$ diameter $d=0\mathrm{.}02m,$

and length $l=0\mathrm{.}1m.$

The number of teeth of Gear $1$: $N_1=48,$ and Gear $2$: $N_2=24,$

Mass moment of inertia of Gear $1,J_1=6*{10}^{-4}kg{m}^2$

Mass moment of inertia of Gear $2,J_2=2*{10}^{-4}kg{m}^2$